From 42442abc6ada474eb8e271ede28f1dcb709cc791 Mon Sep 17 00:00:00 2001 From: nam Date: Thu, 16 Jan 2014 17:49:05 +0900 Subject: [PATCH] Intro copied from various places --- thesis/Makefile | 3 +- thesis/chapters/chap1.tex | 249 ++++++++++++++++++++++++++++++-- thesis/chapters/frontmatter.tex | 52 +++---- thesis/custom_macro.tex | 10 ++ thesis/mythesis.sty | 2 +- thesis/thesis.tex | 28 ++-- 6 files changed, 295 insertions(+), 49 deletions(-) create mode 100644 thesis/custom_macro.tex diff --git a/thesis/Makefile b/thesis/Makefile index a7490a1..b263f10 100644 --- a/thesis/Makefile +++ b/thesis/Makefile @@ -8,14 +8,13 @@ EXTRASTYS = abhepexpt.sty abhep.sty abmath.sty lineno.sty siunitx.sty SIunits.st default: $(TARGET) -$(TARGET): $(INPUT) extrastyles.zip $(THESIS_STY) Makefile +$(TARGET): $(INPUT) extrastyles.zip $(THESIS_STY) Makefile chapters/*.tex @rm -f $(EXTRASTYS) @unzip extrastyles.zip @rm -f $(DOCNAME).{aux,toc,lof,lot} pdflatex $< && bibtex $(DOCNAME) && pdflatex $< && pdflatex $< @rm -f $(DOCNAME).{aux,toc,lof,lot} @rm -f $(EXTRASTYS) - #pdflatex --enable-write18 $< && pdflatex $< clean: @rm -f $(EXTRASTYS) diff --git a/thesis/chapters/chap1.tex b/thesis/chapters/chap1.tex index 6d5978c..3804bcc 100644 --- a/thesis/chapters/chap1.tex +++ b/thesis/chapters/chap1.tex @@ -1,20 +1,251 @@ \chapter{Introduction} -\label{chap:SomeStuff} +\label{chap:intro} %% Restart the numbering to make sure that this is definitely page #1! \pagenumbering{arabic} -\section{$\mu - e$ conversion} -\label{sec:_mu_e_conversion} -\section{Motivation} -\label{sec:motivation} +\section{Muon to electron conversion} +\label{sec:_mu_e_conversion} +Charged lepton flavor violation (CLFV) belongs to the class of flavor-changing +neutral currents, which are suppressed at tree level in the Standard Model +(SM) where they are mediated by $\gamma$ and $Z^0$ bosons, but arise at loop +level via weak charged currents mediated by the $W^{\pm}$ boson. Because flavor +violation requires mixing between generations, CLFV exactly vanishes in the SM +with massless neutrinos. Even in the framework of the SM with massive neutrinos +and their mixing, branching ratio of CLFV is still very small - for example, in +case of \mueg~\cite{marciano}: +\begin{equation} + \mathcal{B}(\mu^{+} \rightarrow e^{+}\gamma) \simeq + 10^{-54} \left( \frac{sin^{2}2\theta_{13}}{0.15}\right) +\end{equation} +This is an unobservably tiny +branching ratio so that any experimental evidence of CLFV would be a clear +sign of new physics beyond the SM. + +One of the most prominent CLFV processes is +a process of coherent muon-to-electron conversion ($\mu +- e$ conversion) in the field of a nucleus: \muecaz. When muons are stopped in +a target, they are quickly +captured by atoms ($~10^{-10}$ s) and cascade down to the 1S orbitals. There, +they can undergo: +(a) ordinary decay, (b) weak capture, $\mu^- p \rightarrow \nu_\mu n$, or (c) +$\mu - e$ conversion, \muec. The last of these reactions is a CLFV process +where lepton flavor numbers, $L_\mu$ and $L_e$, are violated by one unit. + +The $\mu - e $ conversion is attractive both from theoretical and experimental +points of view. Many extensions of the SM predict that it would has sizeable +branching ratio~\cite{altman}. One possible supersymmetric contribution to the +$\mu - e$ conversion is shown in Fig.~\ref{fig:susy_contr}. Experimentally, the +simplicity and distinctive signal, a mono-energetic electron of energy $E_{e}$: +$ + E_{e} = m_{\mu} - B_{\mu}(Z, A) - R(A) \simeq \textrm{105 MeV}, +$ +where $m_\mu$ is the muon mass, $B_\mu(Z, A)$ is the muonic atom binding +energy, and $R(A)$ is the nuclear recoil energy, allow experimental searches +without accidentals and thus in extremely high rates. As a result, one of the +best upper limits of CLFV searches comes from a search for $\mu - e$ conversion +in muonic gold done by the SINDRUM--II collaboration: +\sindrumlimit~\cite{sindrumii}. + +\begin{figure}[tbh] + \centering + \includegraphics[width=\textwidth]{figs/susy_contr} + \caption{Possible SUSY contributions to the CLFV processes \mueg + (left) and \muec (right).} + \label{fig:susy_contr} +\end{figure} + +%\section{Motivation} +%\label{sec:motivation} \subsection{COMET experiment} + +At the Japan Proton Accelerator Research Complex (J-PARC), an experiment to +search for \muec~conversion, which is called COMET (COherent Muon to Electron +Transition), has been proposed~\cite{comet07}. The experiment received Stage--1 +approval in +2009. Utilising a proton beam of 56 kW (8 GeV $\times$ 7 $\mu$A) from the +J-PARC main ring, the COMET aims for a single event sensitivity of $3 \times +10^{-17}$, which is 10000 times better than the current best +limit at SINDRUM--II. As of April 2013, the COMET collaboration has 117 +members in 27 institutes from 12 countries. + +The COMET experiment is designed to be carried out at the Hadron +Experimental Facility using a bunched proton beam that is +slowly-extracted from the J-PARC main ring. The experimental set-up consists of +a dedicated proton beam line, a muon beam transport section, and a detector +section. The muon beam section is composed of superconducting magnets: pion +capture solenoid and a pion/muon transport solenoid. The +detector section has a multi-layered muon stopping target, an electron +transport beam line for $\mu - e$ conversion signals, +followed by detector systems. + +The COMET collaboration has adopted a staging approach with two +phases~\cite{comet12}. COMET Phase--I is scheduled to +have an engineering run in 2016, followed by a physics run in 2017. Phase--I +should achieve a sensitivity +of $3 \times 10^{-15}$, 100 times better than that of SINDRUM--II; while +Phase--II will reach a sensitivity of $2.6 \times 10^{-17}$, which is +competitive with the Mu2e project at Fermilab~\cite{mu2e08}. +A schematic layout of the COMET experiment with its two phases is +shown in Fig.~\ref{fig:comet_phase1}, and a schedule for two phases is shown in +Fig.~\ref{fig:sched}. +\begin{figure}[tbh] + \centering +\includegraphics[width=\textwidth]{figs/comet_phase1} +\caption{Schematic layout of the COMET experiment with two phases: Phase--I +(left) and Phase--II (right).} +\label{fig:comet_phase1} +\end{figure} + +\begin{figure}[tbh] + \centering +\includegraphics[width=0.8\textwidth]{figs/sched} +\caption{The anticipated schedule of the COMET experiment.} +\label{fig:sched} +\end{figure} + +COMET Phase--I has two major goals: +\begin{itemize} + \item Background study for the COMET Phase--II by using the actual COMET beam + line constructed at Phase--I, + \item Search for $\mu-e$ conversion with a single event sensitivity of $3 + \times 10^{-15}$. +\end{itemize} + +In order to realize the goals, COMET Phase--I proposes to have two systems of +detector. A straw tube detector and an electromagnetic calorimeter will be used +for the background study. For the $\mu-e$ conversion search, a cylindrical +drift chamber (CDC) will be built. + \subsection{Proton emission issue} +We, as a jointed force between Mu2e and COMET, would like to measure rates and +energy spectrum of charged particle emission after nuclear muon capture on +aluminum. The rates and spectra of charged particle emission, in particular +protons, is very important to optimize the detector configuration both for the +Mu2e and COMET Phase-I experiments. + +\noindent The tracking chambers of COMET Phase-I and Mu2e are designed to be +measure charged particles of their momenta greater than 70 MeV/$c$ and 53 +MeV/$c$ respectively. In that momentum ranges, it turns out that single hit +rates of the tracking chambers would be dominated by protons after nuclear muon +capture. +The second source of the hit rate will be electrons from muon decays in orbit +(DIO). In order to limit the single hit rate of the tracking chamber to an +acceptable level, both experiments are considering to place proton absorbers in +front of the tracking chambers to reduce proton hit rates. However, the proton +absorber would deteriorate the reconstructed momentum resolution of electrons +at birth. And similarly the rate of proton emission is important to determine +thickness of the muon stopping target made of aluminum. Therefore it is +important to know the rate so that the detector system can be optimized in +terms of both hit rate and momentum resolution. + +\noindent Unfortunately the yield, energy spectrum and composition of the +charged particles emitted in muon capture on Al and Ti have not been measured +in the relevant energy range for COMET Phase-I and Mu2e. +Figure~\ref{fg:silicon-proton} shows the spectrum of charged particle emission +from muons being stopped and captured in a silicon detector \cite{sobo68}. The +peak below 1.4 MeV is from the recoiling heavy ions, mainly $^{27}$Al, when no +charged particles were emitted. Hungerford~\cite{hung34} fitted the silicon +spectrum in Fig.~\ref{fg:silicon-proton} with an empirical function given by +% +\begin{equation} p(T) = A(1-{T_{th} \over T})^{\alpha} e^{-(T/T_0)} + \label{eq:protons} \end{equation} +% +where $T$ is the kinetic energy and the fitted parameters are $A=0.105$ +MeV$^{-1}$, $T_{th}$ = 1.4 MeV, $\alpha$=1.328 and $T_0$ = 3.1 MeV. The +spectrum is normalized to 0.1 per muon capture. Some other results in the past +experiments are summarized in Table~\ref{tb:proton}. + +%\begin{figure}[htb] + %\centering + %\includegraphics[width=0.7\textwidth]{figs/si-proton.pdf} + %\caption{Charged particle spectrum from muons stopping and being captured in + %a silicon detector~\cite{sobo68}.} + %\label{fg:silicon-proton} +%\end{figure} + + +\begin{table}[htb] + \centering \caption{Probabilities in unites of $10^{-3}$ per + muon capture for inclusive proton emission calculated by Lifshitz and + Singer~\cite{lifshitz80}. + The numbers in crescent parenthesis are estimates for the total inclusive + rate derived from the measured exclusive channels by the use of the + approximate regularity, such as $(\mu, \nu p):(\mu, \nu p n):(\mu, \nu p + 2n):(\mu, \nu p 3n) = 1:6:4:4$.} + \label{tb:proton} + \vskip 3mm + \begin{tabularx}{\textwidth}{ccccX} + \toprule + Target nucleus & Calculation & Experiment & Estimate & Comments \\ + \midrule + %$_{10}$Ne & & $200\pm 40$ & & \\ + $^{27}_{13}$Al & 40 & $>28 \pm 4$ & (70) & 7.5 for $T>40$ MeV \\ + $^{28}_{14}$Si & 144 & $150\pm30$ & & 3.1 and 0.34 $d$ for $T>18$ MeV \\ + $^{31}_{15}$P & 35 & $>61\pm6$ & (91) & \\ + $^{46}_{22}$Ti & & & & \\ + $^{51}_{23}$V & 25 & $>20\pm1.8$ & (32) & \\ + \bottomrule + \end{tabularx} +\end{table} + +\noindent The limited information available at present makes it difficult to +draw quantitative conclusive detector design. From Table~\ref{tb:proton}, the +yield for Al can be taken from experiment to be $>$3\% for $T>40$ MeV, or from +theory to be 4\%, or estimated based on the ratio of exclusive channels from +other nuclei to be 7\%, or speculated to be as high as Si +%or Ne +, namely 15-20\%. The +energy spectrum can only be inferred from the Si data or from +Ref.~\cite{bala67}. At this moment, for both COMET Phase-I and Mu2e, this +analytical spectrum has been used to estimate proton emission. And also the $p, +d, \alpha$ composition is not known. The Ti proton yield can only be estimated +from V to be around 3\%. + +\noindent It might be worth to present how proton emission affects a single +rate of the tracking chambers. As an example for COMET Phase-I, single rates +of the tracking chamber (cylindrical drift chamber) have been simulated based +on the spectrum given in Eq.(\ref{eq:protons}). To reduce protons entering the +tracking chamber, in addition to the inner wall of the drift chamber (of 400 +$\mu$m) a cylindrical proton absorber of different thickness is located in +front of the tracking chamber. Monte Carlo simulations were done with three +different thickness of proton degrader, namely 0~mm, 5~mm, and 7.5~mm. +%Figure~\ref{fig:protongenerated} shows a proton momentum spectrum generated +(larger than 50 MeV/$c$) in the simulation study, and regions in red show +protons reaching the first layer. The results are summarized in +Table~\ref{tb:protonhits}, where the proton emission rate of 0.15 per muon +capture is assumed. If we assume the number of muons stopped in the +muon-stopping target is $5.8 \times 10^{9}$/s, the number of muon capture on +aluminum is about $3.5 \times 10^{9}$/s since the fraction of muon capture in +aluminum is $f_{cap}=0.61$. Therefore the total number of hits in all the cells +in the first layer is estimated to be 530 kHz (1.3 MHz) for the case of a +proton degrader of 5 mm (0 mm) thickness. This example present the importance +to understand the proton emission, rate and spectrum, from nuclear muon capture +on aluminum for COMET Phase-I and Mu2e. +% +\begin{table}[htb] + \begin{center} + \caption{Total numbers of hits in the first + layer by protons emitted from muon capture for different trigger counter + thickness. 100 k proton events were generated for COMET Phase-I. 15 \% + protons per muon capture is assumed.} + \label{tb:protonhits} + \vspace{5mm} + \begin{tabular}{lccc} + \toprule + Proton degrader thickness & 0 mm & 5 mm& 7.5 mm\\ + \midrule +% number of 1 hit events & 2467 & 87 & 28 \cr\hline number of 2 hit events & +% 73 & 8 & 1 \cr\hline number of 3 hit events & 9 & 0 & 0 \cr\hline\hline +% number of 4 hit events & 1 & 0 & 0 \cr\hline\hline + Hits & 2644 & 103 & 30 \cr + Hits per proton emission & 2.6 \% & 0.1 \% & 0.03 \% \cr + Hits per muon capture & $3.9\times10^{-3}$ & $1.5\times10^{-4}$ & $4.5\times10^{-5}$ \cr + \bottomrule + \end{tabular} + \end{center} +\end{table} \subsection{Any physics implication??} -% section motivation (end) - - - % section _mu_e_conversion (end) diff --git a/thesis/chapters/frontmatter.tex b/thesis/chapters/frontmatter.tex index 6ccc7ac..28a4524 100644 --- a/thesis/chapters/frontmatter.tex +++ b/thesis/chapters/frontmatter.tex @@ -1,46 +1,46 @@ %% Title -\titlepage[of Churchill College]% -{A dissertation submitted to the University of Cambridge\\ - for the degree of Doctor of Philosophy} +\titlepage[of Graduate School of Science]% +{A dissertation submitted to the Osaka University\\ +for the degree of Doctor of Philosophy} %% Abstract \begin{abstract}%[\smaller \thetitle\\ \vspace*{1cm} \smaller {\theauthor}] - %\thispagestyle{empty} - \LHCb is a \bphysics detector experiment which will take data at - the \unit{14}{\TeV} \LHC accelerator at \CERN from 2007 onward\dots + %\thispagestyle{empty} + \LHCb is a \bphysics detector experiment which will take data at + the \unit{14}{\TeV} \LHC accelerator at \CERN from 2007 onward\dots \end{abstract} %% Declaration \begin{declaration} - This dissertation is the result of my own work, except where explicit - reference is made to the work of others, and has not been submitted - for another qualification to this or any other university. This - dissertation does not exceed the word limit for the respective Degree - Committee. - \vspace*{1cm} - \begin{flushright} - Andy Buckley - \end{flushright} + This dissertation is the result of my own work, except where explicit + reference is made to the work of others, and has not been submitted + for another qualification to this or any other university. This + dissertation does not exceed the word limit for the respective Degree + Committee. + \vspace*{1cm} + \begin{flushright} + Andy Buckley + \end{flushright} \end{declaration} %% Acknowledgements \begin{acknowledgements} - Of the many people who deserve thanks, some are particularly prominent, - such as my supervisor\dots + Of the many people who deserve thanks, some are particularly prominent, + such as my supervisor\dots \end{acknowledgements} %% Preface \begin{preface} - This thesis describes my research on various aspects of the \LHCb - particle physics program, centred around the \LHCb detector and \LHC - accelerator at \CERN in Geneva. + This thesis describes my research on various aspects of the \LHCb + particle physics program, centred around the \LHCb detector and \LHC + accelerator at \CERN in Geneva. - \noindent - For this example, I'll just mention \ChapterRef{chap:SomeStuff} - and \ChapterRef{chap:MoreStuff}. + \noindent + For this example, I'll just mention \ChapterRef{chap:SomeStuff} + and \ChapterRef{chap:MoreStuff}. \end{preface} %% ToC @@ -49,6 +49,6 @@ %% Strictly optional! \frontquote{% - Writing in English is the most ingenious torture\\ - ever devised for sins committed in previous lives.}% - {James Joyce} + Writing in English is the most ingenious torture\\ +ever devised for sins committed in previous lives.}% +{James Joyce} diff --git a/thesis/custom_macro.tex b/thesis/custom_macro.tex new file mode 100644 index 0000000..e154a38 --- /dev/null +++ b/thesis/custom_macro.tex @@ -0,0 +1,10 @@ + +\newcommand{\lagr}{\cal{L}} +\newcommand{\mueg}{$\mu^{+} \rightarrow e^{+}\gamma$} +\newcommand{\meee}{$\mu \rightarrow eee$} +\newcommand{\muenn}{$\mu \rightarrow e \nu \overline{\nu}$} +\newcommand{\muenng}{$\mu \rightarrow e \nu \overline{\nu} \gamma$} +\newcommand{\muec}{$\mu^{-} N \rightarrow e^{-} N$} +\newcommand{\muecaz}{$\mu^{-} + N(A,Z) \rightarrow e^{-} + N(A,Z)$} +\newcommand{\sindrumlimit} +{$\mathcal{B} (\mu^- + Au \rightarrow e^- +Au) < 7\times 10^{-13}$} diff --git a/thesis/mythesis.sty b/thesis/mythesis.sty index 88624aa..9a1c6db 100644 --- a/thesis/mythesis.sty +++ b/thesis/mythesis.sty @@ -1,4 +1,4 @@ -\ProvidesPackage{thesis}[2005/07/28] +\ProvidesPackage{mythesis}[2005/07/28] %\RequirePackage{timing} \RequirePackage{hepnicenames,abhep} % \RequirePackage{siunitx} diff --git a/thesis/thesis.tex b/thesis/thesis.tex index 85fd058..b7a2c48 100644 --- a/thesis/thesis.tex +++ b/thesis/thesis.tex @@ -1,6 +1,11 @@ \documentclass{mythesis} \usepackage{mythesis} +\usepackage{hyperref} +\usepackage{booktabs} +\usepackage{tabularx} +\usepackage{color} +\input{custom_macro.tex} %% You can set the line spacing this way %\setallspacing{double} %% or a section at a time like this @@ -10,17 +15,18 @@ \makeatletter \@ifpackageloaded{hyperref}{% \hypersetup{% -pdftitle = {Studying B to K pi decays with LHCb}, -pdfsubject = {Andy Buckley's PhD thesis}, -pdfkeywords = {LHCb, B, physics, LHC, heavy flavour}, -pdfauthor = {\textcopyright\ Andy Buckley} + pdftitle = {A Study of Muon Capture for Muon to Electron Conversion + Experiments}, + pdfsubject = {Nam H Tran's PhD thesis}, + pdfkeywords = {muon capture, muon to electron conversion, COMET}, + pdfauthor = {\textcopyright\ Nam Hoai Tran} } }{} \makeatother %% Define the thesis title and author -\title{A study of \BToKPi decays with\\ the \LHCb experiment} -\author{Andrew Gordon Buckley} +\title{A Study of Muon Capture for \\Muon to Electron Conversion Experiments} +\author{Nam Hoai Tran} %% Start the document \begin{document} @@ -34,11 +40,11 @@ pdfauthor = {\textcopyright\ Andy Buckley} \begin{mainmatter} %% Actually, more semantic chapter filenames are better, like "chap-bgtheory.tex" \input{chapters/chap1} - \input{chapters/chap2} - \input{chapters/chap3} - \input{chapters/chap4} - \input{chapters/chap5} - \input{chapters/chap6} + %\input{chapters/chap2} + %\input{chapters/chap3} + %\input{chapters/chap4} + %\input{chapters/chap5} + %\input{chapters/chap6} %% To ignore a specific chapter while working on another, %% making the build faster, comment it out like this: %\input{chapters/chap4}